Maximum power output circuit for an EHC and design method thereof

ABSTRACT

A maximum power output circuit for EHC and its design method are presented. The circuit is comprised of a magnetic core, that is, a primary coil and a secondary coil, with a load resistor and a capacitor parallel connected at the two ends of the secondary coil. The circuit enables the EHC to be always working at the maximum power output, thus realizing maximum power output of the energy harvesting power source.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Chinese Application No.201510111209.X, filed on Mar. 13, 2015, the content of which is herebyincorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to transmission line technology, and inparticular relates to a maximum power output circuit for an EHC and adesign method thereof.

Background Information

For real time monitoring of grid assets and effective reduction of gridfaults, online grid monitoring systems are extensively developed at homeand abroad. FIG. 1 shows the structure of such a system, where amonitoring device is directly installed on the power transmission linefor monitoring of inclination angle, stress, conductor temperature andconductor current, the monitoring data thereof being transmittedwirelessly to a monitoring platform, which then accesses the status ofthe power transmission line with combined inputs of monitored parametersand running status of the transmission line. Practices in recent yearsshow that power supply and communication are two bottlenecks impedingdevelopment of online monitoring solutions for power transmission lines.

Up to now, of mature harvesting solutions there are mostly solar energy,wind power, capacitive divider, laser supply, induction harvesting,differential temperature harvesting, and vibration harvesting. Bycomparison of the above-mentioned harvesting solutions, inductionharvesting is believed to be the most suitable for transmission lineenergy harvesting. USI, OTLM, Hangzhou Thunderbird, and Xi'an Jinyuanhave all developed commercial products based on induction harvesting.However, all the above products work on the range in excess of 50 A dueto limited power supply, and hence are prevented from operating normallyon most applications generally with a working current below 50 A.

For an online monitoring power source for power transmission line, itneeds to be capable of adapting to big load swings in addition to posingno risk for the transmission line per se. Thus, an induction harvestingsolution shall meet the following requirements for: {circle around (1)}large dynamic range; current over a power transmission line ranges froma peak current over 1000 A to a valley one of 40 A and even as low as 10A for certain distribution networks; output power of an energyharvesting coil (hereunder abbreviated as EHC) is positively correlatedwith the current on the transmission line; as is shown on FIG. 2, theoutput power of the EHC needs to be regulated via practical means toconsistently output a stable power within the wide dynamic range;{circle around (2)} high density per unit power; the weight of an onlinemonitoring device is strictly regulated due to safety considerations,for example, the weight of a universal monitoring device is limited to2.5 kg, that of a vibration monitoring is limited to 1 kg, and that fora distribution network monitoring device is limited to 500 g; therefore,the only way to solve the problem is to increase the power density ofthe energy harvester; and {circle around (3)} anti-surge capability; atransmission line is subject to impact of short circuits or lightning,which might result in a peak current of several kA, so the inductionharvester shall be able to withstand such current surges.

Foreign and domestic scholars focus their research mostly on twoaspects, power output model and protection of the EHC. N. M. Roscoe, M.D. Judd, L. Fraser, “A novel inductive electromagnetic energy harvesterfor condition monitoring sensors,” in Proc. Int. Conf. Condit. Monitor.Diagnosis, Sep. 2010, pp. 615-618, N. M. Roscoe, M. D. Judd, and J.Fitch, “Development of magnetic induction energy harvesting forcondition monitoring,” in Proc. 44th Int. Univ. Power Eng. Conf.,September 2009, pp. 1-5, N. M. Roscoe, Judd M. D. Harvesting energy frommagnetic fields to power condition monitoring sensors.” IEEE Sensors J.,vol. 13, no. 6, pp. 2263-2270, 2013, consider an EHC equivalent to avoltage source or a current source, with output power of the EHCreaching it maximum when load resistance is equal to internal resistanceof the power source. In fact, output voltage of the EHC changes as theload current changes, and as the load of the EHC changes, its outputvoltage and current change simultaneously, and therefore the aboveassumption does not strictly hold.

SUMMARY OF THE INVENTION

The object of the present invention is to overcome the above deficiencyof the prior art and to provide a maximum power output circuit for anEHC and a design method thereof. Said circuit enables the EHC to bealways working at the maximum output power point, raises the maximumpower density of the harvester, and realizes maximum power output of theharvester.

The technical solution of the present invention is as follows:

A maximum power output circuit for an EHC, characterized in that it iscomprised of a magnetic core, that is, a primary coil (N1) and asecondary coil (N2), with a load resistor (R) and a capacitor (C)parallel connected at two ends of the secondary coil.

A design method for the above maximum power output circuit for the EHC,characterized in that the method comprises the following steps:

{circle around (1)} setting a power density index λ under a minimumworking current;

{circle around (2)} calculating a magnetization current I_(μ) under theminimum working current according to a maximum output power of theenergy harvesting coil with the following formula:

$I_{\mu} = \sqrt[k]{I_{1}/\left( {C_{1}\left( {k + 1} \right)} \right)}$

where, I_(Fe)=C₁I_(μ) ^(k), C₁ is a transformation coefficient betweenthe hysteresis loss current I_(Fe) and the current I_(μ) parallel to amagnetic flux, and k is a transformation index between the hysteresisloss current I_(Fe) and the current I_(μ) parallel to the magnetic flux,and I₁ is a primary current;

{circle around (3)} selecting a material for the magnetic core, andcalculating an outer parameter D_(o) and a thickness h in accordancewith a density w and a volume V of the magnetic core by the followingformula:

V = π(D_(o)² − D_(i)²)h/4${V = {W/w}},{P_{\max} = {\mu\;{hf}\;\ln\frac{D_{o}}{D_{i}}\left( {{I_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{1}{k}} - {C_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{k + 1}{k}}} \right)}}$

where, V is the fixed volume of the magnetic core, D_(i) is an innerdiameter, W is a weight thereof, P_(max) is a maximum output power, andf is a working frequency;

{circle around (4)} calculating, in accordance with the followingformulas, a load resistance R and a capacitance C:

$\begin{matrix}{R = {E_{2}/I_{R}}} & (13) \\{C = \frac{\left( {I_{\mu} - {I_{1}\cos\;\alpha}} \right)}{E_{2}*2\;\pi\; f*N_{2}}} & (14)\end{matrix}$

where, I_(R) is a current on the load resistor, E2 is an inductionvoltage of a secondary side of the energy harvesting coil, N₂ is anumber of the secondary coil of the energy harvesting coil, μ is aneffective permeability of the magnetic core, I_(μ) is the magnetizationcurrent, I1 is a primary current, f is a frequency of a power source, αis an angle between the primary current I1 and the magnetization currentI_(μ), α=90 degrees.

The underlying principle of the present invention is:

1. CT Harvesting Model

For analysis of power output characteristics of an EHC, a diagram of aload equivalent model established for the EHC on the basis of theelectro-magnetic induction theory is shown on FIG. 3.

Let the current flowing through the conductor line being i_(s), theinner diameter of the EHC being D_(i), its outer diameter being D_(o),its width being h, its turns being N₂, then, the induction voltage E₂ onthe secondary side of the EHC is:

$\begin{matrix}{E_{2} = {N_{2}\frac{\mu\; h}{2\;\pi}\ln\frac{D_{o}}{D_{i}}\frac{d\; I_{\mu}}{d\; t}}} & (1)\end{matrix}$where, μ being the effective magnetic permeability of the magnetic core,I_(μ) being the magnetization current.

It follows from the magnetic potential balance equation that:İ ₁ N ₁ +İ ₂ N ₂ =İ _(m) N ₁  (2)where, N₁ being the number of the primary turns, and is set as 1 here,N₂ being the number of the secondary turns, I_(m) being the excitingcurrent.

Take into account of hysteresis loss, the exciting current İ_(m) can bedecomposed into a current İ_(μ) parallel to the magnetic flux and ahysteresis loss current İ_(Fe) perpendicular to the magnetic flux,satisfyingİ _(μ) +İ _(Fe) =İ _(m)  (3)

By ignoring the primary and secondary magnetic flux leakage and theinternal resistance of the coil, the vector diagram of the load modelfor the EHC is shown on FIG. 4.

Referring to FIG. 4, İ_(R) being the resistive current component of theload, İ_(c) being the capacitive current component of the load, and thefollowing equations can be deduced from FIG. 4:

$\begin{matrix}{{{{\overset{.}{I}}_{1}\sin\; a} - {{\overset{.}{I}}_{R}N_{2}}} = {\overset{.}{I}}_{Fe}} & (4) \\{{{{\overset{.}{I}}_{1}\cos\; a} + {{\overset{.}{I}}_{C}N_{2}}} = {\overset{.}{I}}_{\mu}} & (5) \\{P^{\prime} = {{\left( {{{\overset{.}{I}}_{1}\sin\;\alpha} - {\overset{.}{I}}_{Fe}} \right)\frac{\mu\; h}{2\;\pi}\ln\frac{D_{o}}{D_{i}}\frac{d{\overset{.}{I}}_{\mu}}{d\; t}} = {\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}{I_{\mu}\left( {{I_{1}\sin\;\alpha} - {C\; I_{\mu}^{k}}} \right)}}}} & (6)\end{matrix}$

The core loss can be calculated according to the empirical Steinmetzformula:P_(v)=C_(m)f^(α)B^(β)  (7)

The core loss per volume Pv is an exponential function of alternatingmagnetizing frequency f and the peak flux density B. C_(m), α, and β areempirical parameters, and the two exponents α and β are in the ranges of1<a<3 and 2<β<3, where the work frequency f is fixed. Thus the core lossper volume is dependent only on the peak flux density B, and byregarding the core hysteresis resistance approximately as R_(m), thenP_(v)=R_(m)I_(Fe) ²  (8)Comparing expression (1) and (3), the hysteresis loss current I_(Fe) canbe expressed as:I_(Fe)=C₁I_(μ) ^(k)  (9)where, C₁ is a transformation coefficient between the hysteresis losscurrent I_(Fe) and the current I_(μ) parallel to the magnetic flux, andk is a transformation index between the hysteresis loss current I_(Fe)and the current I_(μ) parallel to the magnetic flux. By substitutingexpression (9) in expression (6), the output power model of the EHC is:

$\begin{matrix}{P^{\prime} = {\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}{I_{\mu}\left( {{I_{1}\sin\;\alpha} - {C_{1}I_{\mu}^{k}}} \right)}}} & (10)\end{matrix}$It follows from expression (10) that α is an independent variable, theoutput power reaching its maximum when α=90 degrees, with İ_(μ) and İ₁differing by 90 degrees at that point; it follows at the mean time thatthe load of the EHC is capacitive.

Thus the maximal condition for the output power is:

$\begin{matrix}{\frac{d\; P}{d\; I_{\mu}} = {{\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}\left( {{{C_{1}\left( {k + 1} \right)}I_{\mu}^{k}} - I_{1}} \right)} = 0}} & (11)\end{matrix}$

From expression (11) the condition for maximum power output of the EHCis obtained as

${I_{\mu} = \sqrt[k]{I_{1}/\left( {C_{1}\left( {k + 1} \right)} \right)}},$with the maximum power output being:

$\begin{matrix}{P_{m\;{ax}} = {\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}\left( {{I_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{1}{k}} - {C_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{k + 1}{k}}} \right)}} & (12)\end{matrix}$

Solve for I_(μ) from C₁(k+1)I_(μ) ^(k)=I₁, substitute it in expressions(4) and (5) to obtain the maximum power and the resistance andcapacitance values at the maximum power point:

$\begin{matrix}{R = {E_{2}/I_{R}}} & (13) \\{C = \frac{\left( {I_{\mu} - {I_{1}\cos\;\alpha}} \right)}{E_{2}*2\;\pi\; f*N\; 2}} & (14)\end{matrix}$

with the annular magnetic core having a volume of:V=π(D _(o) ² −D _(i) ²)h/4  (15)

By defining the unit output power density A. as the ratio of the outputpower over the volume, it follows that:

$\begin{matrix}{\lambda \propto {I\; n{\frac{D_{o}}{D_{i}}/\left( {D_{o}^{2} - D_{i}^{2}} \right)}}} & (16)\end{matrix}$

It can be seen that by selecting the magnetic core material, fixing itsvolume, the is permeability, and the primary current, the power densityis proportional to

$I\; n{\frac{D_{o}}{D_{i}}/{\left( {D_{o}^{2} - D_{i}^{2}} \right).}}$

In comparison with prior art, the present invention is effective inthat:

The present invention, by demonstrating both theoretically andexperimentally the effects of the magnetic core shape and the number ofsecondary turns on the output power of the EHC, by establishes an outputpower model for the EHC based on the capacitance-resistance model, bymore than doubling its unit power density, by further establishing poweroutput characteristics for the harvester comprising the EHC and thepower management module, and by enabling the EHC to be always working atthe maximum power output point, realizes maximum power output for theEHC.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention description below refers to the accompanying drawings, ofwhich:

FIG. 1 is a schematic diagram of a prior art online monitoring systemfor a power transmission line.

FIG. 2 exhibits a prior art method for controlling the output power ofan EHC to be outputting a stable power output in a wide dynamic range.

FIG. 3 is a schematic diagram of the equivalent load model of the EHC ofthe present invention.

FIG. 4 is a vector diagram of the resistance-capacitance model by takinginto account the hysteresis loss.

FIG. 5 is a schematic diagram of an embodiment of the maximum poweroutput of the EHC of the present invention.

FIG. 6 shows a three dimensional display of a load resistance R of anembodiment of the maximum power output of the EHC of the presentinvention under dynamic adjustment of a sliding rheostat.

DETAILED DESCRIPTION

Referring to FIG. 3, a schematic diagram of the equivalent load model ofthe EHC of the present invention, it can be seen therefrom that themaximum power output circuit of the EHC of the present invention iscomprised of a magnetic core, that is, a primary coil N1 and a secondarycoil N2, with a load resistor R and a capacitor C parallel connected atthe two ends of the secondary coil.

The design method for an embodiment of the maximum power output circuitof the EHC of the present invention comprises the following steps:

1) setting the power density λ of the magnetic core as 1.38 mW/g@10 A,that is, requiring the 1 kg magnetic core be capable of outputting 1380mW power with a 10 A primary current;

2) selecting silicon steel as the material for the magnetic core of theembodiment, with a density of 7.35 g/cm³, C₁ being 0.22, k being 0.95,the effective permeability being 0.01, I₁=10 A, and obtaining I_(μ) as27.5 A according to

${I_{\mu} = \sqrt[k]{I_{1}/\left( {C_{1}\left( {k + 1} \right)} \right)}};$

substituting I_(μ) in

${P_{m\;{ax}} = {\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}\left( {{I_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{1}{k}} - {C_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{k + 1}{k}}} \right)}},$to obtain the maximum power output as

${67.02*h\;\ln\frac{D_{o}}{D_{i}}},$with the power density for the magnetic core being:

$\lambda = {67.02*h\;\ln{\frac{D_{o}}{D_{i}}/\left( {{\pi\left( {D_{o}^{2} - D_{i}^{2}} \right)}{h/4}} \right)}}$

3) setting the inner diameter of the magnetic core Di as 55 mm, itsweight as 450 g, with λ>1.2 mW/g, an calculation would show thatD_(o)<75 mm

The shape of the magnetic core shall be as D₀=75 mm, D_(i)=55 mm, h=30mm,

4)

$\begin{matrix}{R = {E_{2}/I_{R}}} & (13) \\{C = \frac{\left( {I_{\mu} - {I_{1}\cos\;\alpha}} \right)}{E_{2}*2\;\pi\; f*N\; 2}} & (14)\end{matrix}$

Calculations with expressions (13) and (14) will obtain C=17.1 uF, andR=1050 ohm.

Parameters Value Density 7.35 g/cm3 Turns 200 μ 0.01 C1 0.22 K 0.95

The experiment model is shown on FIG. 5. The current of the currentgenerator is set as 10 A, the load capacitance C is increased in stepsstarting from 0 to 5 uF, the load resistor R is dynamically adjusted viaa sliding rheostat, with the power output on the load resistor beingdisplayed on FIG. 6, wherefrom it can be known that the maximum poweroutput is 600 mW, conforming to theoretical calculation.

The invention claimed is:
 1. A maximum power output circuit for anenergy harvesting coil, comprising a primary coil, the primary coilbeing a magnetic core having an outer parameter D₀, an inner diameterD_(i), a width h, a density w, a weight W, an effective permeability μ,a maximum power output P_(max), and a fixed volume V, a secondary coil,the secondary coil being wound around the primary coil with N₂ number ofturns, a load resistor having a resistance R, and a capacitor having acapacitance C, wherein the load resistor and the capacitor areseparately parallel connected to two ends of the secondary coil; themagnetic core has the fixed volume V beingV = π(D_(o)² − D_(i)²)h/4  and V = W/w, and${P_{m\;{ax}} = {\mu\; h\; f\;\ln\frac{D_{o}}{D_{i}}\left( {{I_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{1}{k}} - {C_{1}\left( \frac{I_{1}}{C_{1}\left( {k + 1} \right)} \right)}^{\frac{k + 1}{k}}} \right)}},$wherein f is a frequency of a power source, I₁ is a primary current, C₁is a transformation coefficient between a hysteresis loss current I_(Fe)and a current I_(μ) parallel to a magnetic flux, and k is atransformation index between the hysteresis loss current I_(Fe) and thecurrent I_(μ) parallel to the magnetic flux; the load resistor has theresistance R beingR=E ₂/I _(R,) wherein E₂ is an induction voltage of a secondary side ofthe energy harvesting coil, and I_(R) is a current on the load resistor;and the capacitor has the capacitance C being${C = \frac{\left( {I_{\mu} - {I_{1}\cos\;\alpha}} \right)}{E_{2}*2\;\pi\; f*N_{2}}},$wherein α is an angle of 90 degrees between the primary current I₁ andthe magnetization current I_(μ).
 2. A method for designing the maximumpower output circuit for the energy harvesting coil of claim 1,comprising setting a power density index λ under a minimum workingcurrent; calculating the magnetization current I_(μ), under the minimumworking current according to a maximum output power of the energyharvesting coil as follows:$I_{\mu} = \sqrt[k]{I_{1}/\left( {C_{1}\left( {k + 1} \right)} \right)}$andI_(Fe)=C₁I_(μ) ^(k), selecting a material for the magnetic core andcalculating the outer parameter D_(o) and the width h in accordance withthe density w and the volume V of the magnetic core calculating theresistance R and selecting the load resistor having the resistance R;and calculating the capacitance C and selecting the capacitor having thecapacitance C.